Generalized linear quadratic regulator design for systems with time delays

A generalized linear quadratic regulator (GLQR) design is formulated to treat a special class of LTI systems where the feedback control law K(z) contains a time-delay operator z. The state weighting matrix Q(z) is no longer real but may be a matrix of polynomials in z. In this case, the forward and inverse GLQR designs can be partly resolved by using algorithms developed from the generalized linear system theory. Some results of the GLQR formulations for single-input single-output systems using the Chyung-Morse-type controllers are also presented.<>